Sound in Ducts

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Sound in Ducts

Transcript of Sound in Ducts

Noise and Vibration Control

4. SOUND IN DUCTS

Indian Institute of Technology Roorkee

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Noise and Vibration Control

Many technical systems involve the transport of a liquid or a gas, i.e., pipe, duct, or channel flow. Examples :cooling water in a nuclear power plant, exhaust gases from an internal combustion engine, or fresh air in a ventilation system. Because the source is primarily designed to perform a more meaningful task than the generation of sound (e.g., to drive an automobile in the case of an automobile engine), and is usually already designed and built when the noise problem is discovered, the required solution is a modification to the duct system. Hindrances provided to counter the transmission of sound are commonly called mufflers or silencers, depending on the context. Indian Institute of Technology Roorkee

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Noise and Vibration Control Silencer - an element in the flow duct that acts to reduce the sound transmitted along the duct while allowing free flow of the gas through the flow passage.

Indian Institute of Technology Roorkee

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Noise and Vibration Control

Passive silencer : the sound is attenuated by reflection and absorption of the acoustic energy within the element. reactive: reflection of sound waves (i) side branch muffler or resonator chamber muffler and (ii) expansion chamber muffler -dissipative : dissipation/ absorption of acoustic energy Active silencer : the noise is canceled by electronic feed forward and feedback techniques.

Indian Institute of Technology Roorkee

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Noise and Vibration Control

Indian Institute of Technology Roorkee

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Noise and Vibration Control Muffler design coupled problem treatment: (i) sound source (fan, internal combustion engine, compressor); (ii) duct system (ventilation channel, exhaust gas system, air pressure duct); (iii) termination (register, exhaust gas outlet, nozzle).note : in cases where the source and termination are reflection-free, the coupling is small - design can be based on an analysis of the transmission properties of the muffler. transmission isolation (DTL), - ratio of the incident to the transmitted sound power when the muffler is connected to a reflection-free termination

DTL = 10 log(Wi Wt )

insertion loss (DIL) - where the sound pressure at some point in the duct system (outlet), is compared for two different muffler configurations A and B, DIL = 20 log p B p A

Indian Institute of Technology Roorkee

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Noise and Vibration Control Muffler performance requirements: (i) right outer geometry; (ii) low pressure drop; (iii) sufficient sound attenuation (i) demands on the outer geometry normally, besides limiting the total volume, also imply a specific outer form. example- passenger cars, in which the muffler is often to be located behind the rear axle, adjacent to the reserve tire. (ii) The demand for a small pressure drop, which is proportional to the square of the average flow velocity, U2, is driven by operating costs of the complete system. For passenger car, the pressure drop across the entire exhaust system is of the order of magnitude 300 mbar, and since the corresponding volume flow is 10 m3/min, the power loss is about 7.5 hp . Indian Institute of Technology Roorkee7/46

Noise and Vibration Control

Figure 1 Modern luxury class passenger cars have mufflers with very complex structures, in order to be able to fulfill the stringent comfort demands

Indian Institute of Technology Roorkee

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Noise and Vibration Control

Both of these demands are, of course, secondary to the last-mentioned, primary demand for adequate sound attenuation. That can be formulated in a more or less detailed way, as a specification for a maximum A-weighted sound level measured at the outlet, or as a narrow band specification curve. From these specifications, the muffler design task can be formulated as follows: arrive at a construction that, within a certain volume of space, gives the desired attenuation without overloading the source.

Indian Institute of Technology Roorkee

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Noise and Vibration Control 4.1 Sound Propagation In Ducts sound in channels - straight, cylindrical tube. L>>D; Therefore, below a certain frequency the sound pressure is nearly constant over the cross section. plane wave region: Frequency region where the only modes or propagating waves, that can exist are those that can vary longitudinally. At frequencies above the plane wave region, more complicated wave forms arise; For each of these higher modes, there is a bounding frequency (cut-on frequency), below which the wave is strongly damped. In the plane wave region, the higher modes can only exist locally, in the vicinity of geometric discontinuities.

Indian Institute of Technology Roorkee

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Noise and Vibration Control

Figure 2 Reactive muffler with 2 cavities and no flow restriction -Low cost --Lower back pressure

Indian Institute of Technology Roorkee

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Noise and Vibration Control

Figure 3 Reactive muffler with no direct passage between the inlet and exit -More attenuation --High back pressure affects engine performance

Indian Institute of Technology Roorkee

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Noise and Vibration Control Typical property of sound propagation in a duct - the difference in phase velocity between waves traveling upstream and waves traveling downstream.y r U x zFigure 4 Cross section of a straight duct with its coordinate system. The average flow velocity of the fluid is U.

D

Indian Institute of Technology Roorkee

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Noise and Vibration ControlThe modified wave equation Assumptions: i. Assume small disturbances ii. Ignore the viscosity and heat transfer within the fluid assuming that the steady flow rate is constant over the cross section, The particle velocity is :

r r r r r ut (r , t ) = (U + u x )ex + u y e y + u z ezThe linearized continuity equation :

r + 0 u = 0 +U x tthe linearized equation of motion:

r r u u 0 + U + p = 0 x tIndian Institute of Technology Roorkee

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Noise and Vibration Controlmodified wave equation for the flowing fluid within channel1 p p=0 +U 2 t x c2 2

- can be solved by separation of variables. - therefore assume a solution analogous to

p = p ( y, z ) e ik x x e itin which the exponential factors correspond to wave propagation along the channel. From above equations:

2 2 ( 2 + 2 ) + (k 2 + 2 Mkk x + M 2k 2 k 2 ) = 0 x x y zSet the expression inside the second parentheses to a2; then,

(

2 y 2

+

2 z 2

) + 2 = 0

Indian Institute of Technology Roorkee

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Noise and Vibration Control

For every higher mode, there is a limiting frequency, beneath which the longitudinal wave number becomes complex, and the mode is therefore exponentially damped; That frequency is the modes cut-on frequency. At low enough frequencies, only the plane wave propagates in the channel; all higher modes are strongly attenuated, i.e., cut-off. As the frequency increases and the sound wavelength falls beneath the channel cross-sectional dimensions, more and more higher modes can propagate. That is of great significance to the design of reactive sound mufflers, since a large number of higher propagating modes afford a greater opportunity for sound energy to pass through the muffler.

Indian Institute of Technology Roorkee

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Noise and Vibration Control

Rectangular cross sectionb

h

Circular cross sectionc f 01 = 1.841c Dc f 02 = 3.054 c D_ +

D

c f 10 = c 2b

+_

_

c f 01c f11

= c 2h12

+

_ + + _

1 c 1 = 2 + 2 2b h c f 02

_ ++ _

+ _

c f 10 = 3.832 c D+

+ _

=c b

c f 03 = 4.201 c D

+_ _ + +__+ +_ _ + _ +

c f 20c f 21

=c h1 c 4 = + 2 b2 h2 12

+ _ +_ + _ + _ +c 11

f

c 04

= 5.318 c D

f = 5.331 c D

+_ +_

Table 1 Cut-on-frequencies of the lowest modes of a channel with rigid walls, and rectangular or circular cross section. The dashed lines are nodal lines for sound pressure.

Indian Institute of Technology Roorkee

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Noise and Vibration Control4.2 Reactive silencers and side branch resonators

Assumption: i. for simplicity, the influence of the steady flow is ignored ii. The analysis is limited to the plane wave region

Area discontinuity: an incident wave is partially reflected, and the energy transmitted downstream thereby reduced

Indian Institute of Technology Roorkee

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Noise and Vibration Control

Duct

No reflection

Duct

Reflection at area change

Reflection at duct branch

Figure 5 A sudden change in cross sectional area reflects a portion of the acoustic energy

Indian Institute of Technology Roorkee

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Noise and Vibration Control

S1

S2x

Figure 6 A simple area discontinuity (expansion) is the simplest way to bring about a reflection. The reflection properties of the area discontinuity depend only on the relative cross sectional areas of the incoming and outgoing channels.

Indian Institute of Technology Roorkee

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Noise and Vibration ControlIgnoring any reflections that might occur at discontinuities downstream of the area change, the expressions for the fields upstream and downstream, respectively, are:

p1 = p1+ e ikx + p1 e ikx

+ p 2 = p 2 e ikxin which the time factor eiwt is left out